In modern computer technology, there is a need for monitoring and correcting transient errors in data by means of error correcting code, in particular when writing and reading to and from a memory or other register, such as a database or other storage arrangement. The error correcting code used often follows any previously known or well-recognized algorithm, which may already be part of common general knowledge to skilled persons in the technical field.
An example of such a recognized error correction algorithm is the so-called Reed-Solomon algorithm. This particular error correction algorithm is a coding scheme which operates by first constructing a polynomial from data symbols to be transmitted and then sending an over-sampled plot of the polynomial instead of the original symbols themselves. As a consequence of redundant information contained in the over-sampled data, it is possible to reconstruct the original polynomial and thus the data symbols, even in the face of transmission errors, at least up to a certain degree of error. However, there are several other recognized algorithms that could be suitable for use, and the Reed-Solomon algorithm is just one of these. Other examples include the Hamming code, the Reed-Muller code, the Binary Golay code, convolutional code, various turbo codes and others.
The number of corrections necessary in a set of data is dependent on the error intensity which is accepted or acceptable by the system in which the error correction is applied. An example of this is that fault tolerance must be extremely limited in an aviation system, but other applications, such as telephony or data transmission and also the automotive industry to certain extent, requires low cost solutions. As a trade-off between price and performance in those areas of applicability, certain amounts of inaccuracy may be accepted as long as a low or possibly a medium price level can be maintained in a system.
All error correcting systems introduce certain delays between the transmitter and receiver. In general, an error correction system also deteriorates the over-all performance in any data or communication system. The most spread error correcting code corrects single bit errors and detects multiple bit errors. In information theory and coding, an error correction code, ECC, is defined as a code in which each data signal conforms to specific rules of construction so that departures from this construction in the received signal generally can be detected and corrected automatically. It is used in computer data storage, for example in dynamic RAM, and in data transmission. The simplest error correcting codes are able to correct single-bit errors (single error correction or SEC) and to detect double-bit errors (double error detection or DED). Other codes can detect or correct multiple bit errors.
In the scientific article, “Duplex and Triplex Memory: Which Is More Reliable?”, by Nitin H. Vaidya, department of Computer Science, Texas A&M University, Technical Report 94-025, February 1994, is disclosed an academic study including how replication improves system performance at the cost of increased redundancy. In the article, the reliability of a system using duplication of memory modules is shown to be always worse than simple triplication if the ECC used in the duplex system is capable of only error detection or only single error detection. However, if the ECC is capable of single error detection as well as double error correction, then the duplex system can achieve higher reliability than the triplex system.
In addition to the above, Shannon's theorem is an important theory in error correction which describes the maximum attainable efficiency of an error correction scheme versus the levels of expected interference resulting from noise. If the number of errors is less than or equal to the maximum correctable threshold of the code, all errors will be corrected.
Hence, it can be concluded that all presently known and available error correction codes require more signal elements than are necessary to convey the basic information.